A027569 Initial members of prime decaplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26, p+30, p+32).

11, 33081664151, 83122625471, 294920291201, 573459229151, 663903555851, 688697679401, 730121110331, 1044815397161, 1089869189021, 1108671297731, 1235039237891, 1291458592421, 1738278660731

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

All terms are congruent to 11 (modulo 210). - Matt C. Anderson, May 28 2015

Links

• Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..10000 [first 100 terms from Matt C. Anderson]
• Tony Forbes and Norman Luhn, Prime k-tuplets
• Norman Luhn, 1 million terms of A027569, zip compressed (7.93 MB) (2021)

Crossrefs

Cf. A027570, A202281, A202282.

Programs

Maple

composite_small := proc (n::integer)
description "procedure to determine if n has a prime factor less than 100";
if igcd(2305567963945518424753102147331756070, n) = 1 then
return false else return true end if;
end proc;
# begin initialization section
p := [0, 2, 6, 8, 12, 18, 20, 26, 30, 32]; o := [1271, 1691]; m := 2310;
# end initialization section
with(ArrayTools); os := Size(o, 2); ps := Size(p, 2);
loopstop := 10^11; loopstart := 0;
print(11);
for n from loopstart to loopstop do
for a to os do
counter := 0; wc := 0; wd := 0;
while `and`(wd > -10, wd < ps) do
wd := wd+1;
if composite_small(m*n+o[a]+p[wd]) = false then wd := wd+1 else wd := -10 end if;
end do;
if wd >= 9 then while `and`(counter >= 0, wc < ps) do
wc := wc+1;
if isprime(m*n+o[a]+p[wc]) then counter := counter+1 else counter := -1 end if end do;
end if;
if counter = ps then print(m*n+o[a]); end if;
end do;
end do;
# Matt C. Anderson, Apr 30 2015

PARI

is(n)=isprime(n) && isprime(n+2) && isprime(n+6) && isprime(n+8) && isprime(n+12) && isprime(n+18) && isprime(n+20) && isprime(n+26) && isprime(n+30) && isprime(n+32)
v=primes(10); t=1; forprime(p=31,1e11, v[t]=p; t=(t%10)+1; if(p-v[t]==32 && is(v[t]), print1(v[t]", "))) \\ Charles R Greathouse IV, May 20 2015

Perl

use ntheory ":all"; say for sieve_prime_cluster(1,1e13, 2,6,8,12,18,20,26,30,32); # Dana Jacobsen, Sep 30 2015